Pathology detection and delineation enables the automatic interpretation of medical scans such as chest X-rays while providing a high level of explainability to support radiologists in making informed decisions. However, annotating pathology bounding boxes is a time-consuming task such that large public datasets for this purpose are scarce. Current approaches thus use weakly supervised object detection to learn the (rough) localization of pathologies from image-level annotations, which is however limited in performance due to the lack of bounding box supervision. We therefore propose anatomy-driven pathology detection (ADPD), which uses easy-to-annotate bounding boxes of anatomical regions as proxies for pathologies. We study two training approaches: supervised training using anatomy-level pathology labels and multiple instance learning (MIL) with image-level pathology labels. Our results show that our anatomy-level training approach outperforms weakly supervised methods and fully supervised detection with limited training samples, and our MIL approach is competitive with both baseline approaches, therefore demonstrating the potential of our approach.